No CrossRef data available.
Article contents
Strong convergence of peaks over a threshold
Published online by Cambridge University Press: 23 August 2023
Abstract
Extreme value theory plays an important role in providing approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the generalised Pareto distribution $H_\gamma(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold t, where s(t) is a suitable norming function. We study the rate of convergence of $F_t(s(t)\cdot)$ to $H_\gamma$ in variational and Hellinger distances and translate it into that regarding the Kullback–Leibler divergence between the respective densities.
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust